Bezel and dial

Avoid all cleaning agents of any sort. (Including brown sauce in this case- see earlier despatches). A dial in this state is in danger of losened surface. Using a lint free cloth, or cotton wool, soak as much of the oil up as you can. Don't damp the cloth, just use it dry. DON'T RUB THE DIAL - ONLY DAB IT.

You now need a special rubberised putty called Rodico. (it's a bit like silly putty). Having soaked off the residue you then dab and press the putty all over the dial using a rolling motion to pickup the oil residue. Takes a bit of patience. Don't press too hard as the dial surface might have been disturbed by the oil. Keep dabbing until the oil is removed. DO NOT RUB THE DIAL WITH IT. DAB ONLY. Gradually you should see the the oil diappear and the dial colour restore.

If I have the right chapter ring where are you based?

The dial below was in exactly the same state as yours. The technique I used for this was as described above, With brown sauce afterward. Don't think you should use the brown sauce on your dial.